Ginzburg-Landau Theory for Non-Invertible Symmetry-Breaking Transitions
Abstract
Recently, a generalized Landau paradigm has been proposed, in which a broad class of "unconventional" phase transitions lying beyond the original symmetry-breaking framework of Landau are understood as the symmetry-breaking transitions of generalized symmetries. In particular, in (1+1)D, such "topological" or "deconfined" transitions can be mapped to the symmetry-breaking transitions of non-invertible symmetries. How to extract the universal dynamical properties of the transitions from this understanding? In this paper, we follow the Ginzburg-Landau philosophy and develop a field-theoretic description of such critical points in terms of the fluctuations of local order parameters, now of non-invertible symmetries. The Symmetry Topological Field Theory formalism plays a central role in our analysis, allowing us to identify the algebra of local order parameters from the Lagrangian algebra of a (2+1)D topological order. We illustrate the key ideas and the full steps of this generalized Ginzburg-Landau procedure using the transitions between gapped phases with a simple non-invertible symmetry --- the Rep(S3) symmetry.
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BibTeX
@misc{ravindran2026ginzburglandau,
title = {{Ginzburg-Landau Theory for Non-Invertible Symmetry-Breaking Transitions}},
author = {Vibhu Ravindran and Luisa Eck and Xie Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06751},
eprint = {2609.06751},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06751},
}
RIS
TY - UNPB
TI - Ginzburg-Landau Theory for Non-Invertible Symmetry-Breaking Transitions
AU - Vibhu Ravindran
AU - Luisa Eck
AU - Xie Chen
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06751
UR - https://arxiv.org/abs/2609.06751
AB - Recently, a generalized Landau paradigm has been proposed, in which a broad class of "unconventional" phase transitions lying beyond the original symmetry-breaking framework of Landau are understood as the symmetry-breaking transitions of generalized symmetries. In particular, in (1+1)D, such "topological" or "deconfined" transitions can be mapped to the symmetry-breaking transitions of non-invertible symmetries. How to extract the universal dynamical properties of the transitions from this understanding? In this paper, we follow the Ginzburg-Landau philosophy and develop a field-theoretic description of such critical points in terms of the fluctuations of local order parameters, now of non-invertible symmetries. The Symmetry Topological Field Theory formalism plays a central role in our analysis, allowing us to identify the algebra of local order parameters from the Lagrangian algebra of a (2+1)D topological order. We illustrate the key ideas and the full steps of this generalized Ginzburg-Landau procedure using the transitions between gapped phases with a simple non-invertible symmetry --- the Rep(S_3) symmetry.
ER -